Analysis of a pp-version finite volume method for 1D elliptic problems

In this work, we present and analyze a pp-version finite volume method (FVM) for elliptic problems in the one dimensional setting. Under some regularity assumptions of the exact solution, it is shown that the pp-version FV solution converges with exponential rates under H1,L2H1,L2 and L∞L∞-norms. Superconvergence properties at nodal, Lobatto and Gauss points have been also discussed. Numerical results are presented to support our theoretical findings.